Grenades and gun shots have struck several Islamic targets in France following the murderous attack on the satirical magazine Charlie Hebdo, police and local media said, raising fears of an Islamophobic backlash among the country’s six million-strong Muslim community.

Three grenades hit a mosque in Le Mans, in the early hours of Thursday while in Aude, southern France, two gunshots were fired at an empty prayer room.

A Muslim family in their car in Vaucluse came briefly under fire but escaped unharmed, and a mosque in Poitiers was daubed with graffitti saying “Death to Arabs”. In Villefranche-sur-Saône, an explosion blew out the windows of a kebab shop next door to the town mosque.

On Thursday a delegation of about 20 imams from France’s Muslim federations visited the Charlie Hebdo offices in the 11th arrondissement of Paris and fiercely condemned the gunmen who killed 12 people, including 10 of the magazine’s staff and two police officers.

Witnesses said the gunmen had shouted “Allahu Akbar” and “we have avenged the prophet” as they left the scene after the murders.

“These men are criminals, barbarians, satans. For me, they are not Muslims,” the imam of the Paris suburb of Drancy, said, addressing the media. “Their hatred, their barbarism, has nothing to do with Islam. We are all French, we are all humans. We must live in respect, tolerance and solidarity.”

Abdallah Zakir, president of the Observatory against Islamophobia, told AFP news agency that he was worried that there would be anti-Muslim events. “We’ve had at least three already, and the day is not yet over. I am afraid that these attacks will only spread in the days to come.”

With the Front National’s triumph in last year’s European elections, the growing concerns over large numbers of French jihadis going to Syria and Iraq, and the succession of divisive controversies over Islam and its place in French society, these were, said Dalil Boubakeur, rector of the Grande Mosquée de Paris, not easy times to be a French Muslim.

In a recent interview with Psychologies magazine,Boubakeur suggested French Muslims felt that it was “easier for other populations from abroad – that for them the integration machine works better”. He added: “Our community lacks recognition, it feels it is looked upon with too severe an eye … unjustly attacked.”

French Muslims, he said, were condemned to “eternally divided” lives. “That’s true, above all, for the young, who have the impression of being caught between what they feel they are and what French society would like them to become.”

Coming out of lunchtime prayers at the Adda’wa mosque in the shadow of the Paris ring road, at Porte de la Villette, few worshippers wanted to talk. But many of those who did, braving the cold and driving rain, said they feared they would pay a price for the atrocity.

“People just lump all Muslims together,” said Ali, who worked for Paris city hall. “They associate all Muslims with what those fanatics did. But you’ve seen us here: we are normal people, going back to our jobs. Muslims are not all the same.”

French media have reported that the mosque, housed in a bleak collection of temporary huts while it awaits a more permanent building on a site at its former home in the rue Tanger, used to be regularly frequented by the two suspected gunmen, the brothers Chérif and Saïd Kouachi.

But Ali, who declined to give his full name, said he had gone to the mosque often, for five years at least, and had never seen the pair there.

Another worshipper, Mohammed Aklit, 37, a security guard, said he might have seen the brothers but “years ago, maybe once or twice”.

One man, who refused to be named, said Charlie Hebdo had resorted to publishing cartoons of the Prophet Mohammed – causing uproar in much of the Muslim world – “because they had to sell magazines, they had no money, so that’s they did”. He added: “I reject what happened. But no one should attack the prophet.”

Nourredine, a taxi driver, said the cold-blooded attack on Wednesday at Charlie Hebdo had left him very saddened and angry. It had reminded him of his home country, Algeria, in the 60s and 70s, he said, where “journalists were often the first to be targeted” by extremists.

“But you know, we will become victims of this atrocity,” he said. “There is real stigmatisation in France. I love this country, really I do, but this stigmatization, this amalgamation, this tarring all Muslims with the same brush – all it does is feed the extremists. It helps the Front National, the people who hate and fear Islam.”

Aklit said he was sure the murders at the magazine’s premises would end up fuelling more hatred of Muslims. “Which is just … wrong. Because my Islam, the Islam of so many of us, is a modern, moderate Islam. It’s about communication, respect, tolerance, understanding.”

The French people, Aklit said, shivering under a large green umbrella, were mature and intelligent. “They won’t swallow just anything. They know when they’re being manipulated. But you know that’s just as well, really, because there are plenty out there who will be trying to manipulate this.”